With data on an outcome (Y) and associated covariates (X) jointly available for a modest-sized sample and information on X available for a much larger sample, such a setting can be viewed as missing-data problem. If the association between outcome and covariates is sufficiently strong, the covariates can support precision gains in inferences for the mean of Y. Similarly, with available data on treatment or exposure (T) for the completely-observed cases, precision gains are possible for contrasts involving Y across the levels of T, increasing the effective sample size for inference in a manner similar to including historical controls with randomized-trial data. We use the term “buttressing” to refer to the process of combining an additional sample on X (and possibly T) with data on both X and Y from the perspective that the observed outcomes could support a valid analysis procedure but might be strengthened with the addition of a sample including background covariates. Through simulations across a range of scenarios, we investigate how precision gains from buttressing are linked to the magnitude of the associations between the outcome and background covariates.